Question

A man walks
5.0m
due east and then
10.0m
N30oE
. Find his resultant displacement.
13.7 m,
N15oE
14.6 m,
N20oE
10.0 m,
N15oE
14.6m,
N70oE

Answer 1

Answer on Question #51854, Physics, Mechanics | Kinematics | Dynamics

Question:

A man walks 5.0m due east and then 10.0m N30oE. Find his resultant displacement.

13.7 m, N15oE

14.6 m, N20oE

10.0 m, N15oE

14.6m, N70oE

Answer:

North component of vector equals:

$$d_N = d \cos \theta$$

where $\theta = 30{}^\circ$ – angle between $d$ and north.

East component of vector equals:

$$d_E = d \sin \theta$$

Total displacement to east equals:

$$5 + 10 \sin 30{}^\circ = 10 \, m$$

Displacement to north equals:

$$10 \cos 30{}^\circ = \frac{10\sqrt{3}}{2} \, m = 5\sqrt{3}$$

Resultant displacement equals:

$$D = \sqrt{10^2 + (5\sqrt{3})^2} = 5\sqrt{7} \, m \cong 13.2$$

Angle between $d$ and north equals:

$$\alpha = \arctan \frac{10}{5\sqrt{3}} = 49.1{}^\circ$$

Resultant displacement:

13.2 m N 49.1° E

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